I think this would be possible yes but I see a point where people can disagree:

It is the leader or VLs who set the core list at relations, so IMHO it is perfect for leaders to force fammembers to explore only where he wants.  So it is perfect for a leader to control the family spread, but I think people gonna say this is "Leader Abuse" in the way people has restricted explorations, ...

Now, if this is acepted and implemented, I would strongly recommend to do it the opposite way, so you as leader set the system list your family is ALLOWED to explore, any other system they try to explo outside those cores will get a msg "This system is not allowed by your family leader"

You can say, too much power for a leader, I say real leaders would love this improvement, and they're all advantages for the family, when an attacker wants spread he can check the allowed systems outside the core, so he's always gonna explo according to the leader plan.